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Summary

This activity engages students in the exploration of interference between sinusoidal wave forms. They use an interactive applet to manipulate the phase, wavelength, amplitude, and phase velocity of two waveforms and observe the resulting sum. With an animation button, they can start and stop the motion of the waves.

Context

Audience

This activity is intended for undergraduate students in a physics, mathematics, or mineralogy course that requires an understanding of interaction between sinusoidal wave forms. It may serve as a component of an introduction to Bragg's Law.

Skills and concepts that students must have mastered

Prior to engaging in this activity, students should have a basic understanding of electromagnetic radiation.

How the activity is situated in the course

This activity can serve as an introductory exercise, prior to having students engage in the Bragg's Law activity.

Goals

Content/concepts goals for this activity

Students will gain understanding of the nature of sinusoidal wave interaction.

Higher order thinking skills goals for this activity

Students will learn to visualize mathematical concepts, in this case the summation of two waveforms and how the sum changes as the waves move.

Other skills goals for this activity

Students will learn to predict outcomes based on a mathematical or physical concept.

Description of the activity/assignment

Students interact with an applet to experiment with waveform interference. The activity should be performed in a computer laboratory, with each student at a workstation. They should each be provided with a copy of the following handout, available in Word and pdf format, which they should fill in as they proceed through the exercise. At the completion of the exercise, they should hand it in for grading.

The two green curves are parallel sinusoidal waveforms that have identical wavelengths, amplitudes, and phases when the applet initializes. The blue sinusoidal waveform at the bottom is the sum of the two green parallel waveforms. You can change the phase of the green sinusoidal waveforms by dragging the circles at the left end of the waveform. You can change the wavelength and the amplitude by dragging the other two circles. The sliders to the right of the waveforms offer alternative means of making similar changes.

To animate the waveforms, click on the start button, and to stop the animation, click again. In order to change the speed of the animation of the two green waveforms, you can use the sliders on the lower right, but you must halt the animation in order to adjust the speed. Once your speeds are selected, start the animation again. The speeds are actually phase velocity. In other words, when the two green waveforms animate at equal speeds, each one will advance by an equal number of wavelengths during a given amount of time. Therefore, if they are set to the same speed, but different wavelengths, the waveform with the longer wavelength will advance faster than the other one.

Wave Interference Applet with Initial Settings

Wave Interference Applet with Constructive Interference

We have constructive interference when the wavelength, amplitude, and phase of the two component (blue) waves are identical.

Wave Interference Applet with Destructive Interference

We have destructive interference when the wavelength and amplitude of the two component (blue) waves are identical and the phases differ by 180 degrees.

With the wavelengths and the amplitudes of the component waves identical and their phases different by 90 degrees, there is partial constructive interference.

Wave Interference Applet with a complex sum

With the amplitudes of the two component waves identical and the wavelength of one component wave twice the wavelength of the other, the phase can be adjusted to produce a sum with a more complex form.

Wave Interference Applet with wave beat

With the amplitudes of the two component waves identical and the wavelengths slightly different, the sum exhibits wave beat.

Wave Interference Applet with settings that will result in retrograde wave beat. The start button can be used the initiate an animation that exhibits the retrograde wave beat. On the live applet, click the stop button to halt the animation.

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Glenn Richard, SUNY at Stony Brook

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Glenn Richard, SUNY at Stony Brook

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Glenn Richard, SUNY at Stony Brook

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Glenn Richard, SUNY at Stony Brook

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Glenn Richard, SUNY at Stony Brook

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Glenn Richard, SUNY at Stony Brook

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Glenn Richard, SUNY at Stony Brook

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Glenn Richard, SUNY at Stony Brook

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Glenn Richard, SUNY at Stony Brook

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Glenn Richard, SUNY at Stony Brook

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Glenn Richard, SUNY at Stony Brook

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Glenn Richard, SUNY at Stony Brook

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